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Abstract

We present a new class of KERR-SEN solutions that respect SO(2) symmetry, constructed systematically using the Laurent series expansion method. This approach is based on stationary, axisymmetric Euclidean solutions to the vacuum Einstein equations and incorporates advanced techniques for generating stationary gravitational fields, including the variation-of-constants method and nonlinear superposition. Through this unified framework, we obtain fresh insights into axially symmetric gravitational systems, extend the traditional hierarchy of Kerr-NUT solutions, and bring together several foundational analytic methods under a common structure. The paper offers explicit derivations, supported by numerical simulations, and provides a detailed discussion of the physical consequences, particularly focusing on the roles of dilaton and axion fields. The extended version also includes a comprehensive historical overview of axisymmetric exact solutions, a thorough explanation of the Laurent series formalism in gravitational theory, and an in-depth analysis of the theoretical and astrophysical significance of KERR-SEN metrics in current research.